evaluate expression 1/2a-5b when a= -12 and b= -3

Answer:

-6/7

Step-by-step explanation:

So the question basically is asking, 6x7/15+x=8/7 so find the value of X.

We multiply 7/15 by six because the question says 6 7/15 and we multiply 8 by 1/7 to get 8/7. Hope that was useful!

Answer:Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps

Step-by-step explanation:

Answer:

147 miles

Step-by-step explanation:

Let x be the number of miles travelled on 7 gallons, then proportion is of the form

[tex]\frac{miles}{gallons}[/tex], thus

[tex]\frac{63}{3}[/tex] = [tex]\frac{x}{7}[/tex] ( cross- multiply )

3x = 63 × 7 = 441 ( divide both sides by 3 )

x = 147

Thus the car can travel 147 miles on 7 gallons

Answer:

87/4

Step-by-step explanation:

Step 1:  Convert 21 3/4 into an improper fraction

21 3/4 is same as 21 * 4/4 + 3/4

21 * 4/4 = 84/4

Step 2:  Add them up

84/4 + 3/4

87/4

Answer:  87/4

Answer: 87/4

Step-by-step explanation:

Multiply:

21*4=84

Add:

84+3=87

Your answer should be: 87/4

The denominator stays the same

Answer:

3/10 probability as it is the same as getting 2gm +1rm =3m

Step-by-step explanation:

You add up the numbers 7+2+1=10m

Answer:

4t^2-32t+64=4(t^2-8x+16)

Step-by-step explanation:

f(x)=4x^2-8x+4

f(t-3)=4(t-3)^2 - 8(t-3)+4=

4(t^2-2*t*3+9)-8t+24+4=

4(t^2-6t+9)-8t+28=

4t^2-24t+36-8t+28=

4t^2-32t+64=4(t^2-8x+16)

Rani and her friends can purchase their supplies for $48 after a 20% discount on the original price of $60.

Rani and her friends need to calculate the sale price of the supplies after a 20% discount. The original price is $60, and the discounts amount in money can be determined by multiplying this original cost by 20% or 0.20. This gives you a discount amount of $12. To determine the final price after the discount, you subtract the discount amount from the original price. Therefore: $60 - $12 = $48. Hence, the sale price of the supplies that Rani and her friends need is $48.

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Answer: B, [tex]\sqrt{\frac{1}{6} }[/tex]

Step-by-step explanation:

Using half-angle identities

Using half angle identities, we know that

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-cosx}{2} }[/tex]

Plug in 2/3 for cosx

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-2/3}{2} }[/tex]

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1/3}{2} }[/tex]

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1}{6} }[/tex]

Determining sign

Since the angle x is in quadrant 4 from 270 to 360 degrees, if we divide the angle by 2, the angle x should be somewhere from 135 to 180 degrees, which would all fall in quadrant 2

all sin values in quadrant 2 are positive

Final answer

[tex]sinx = \sqrt{\frac{1}{6} }[/tex]

If cos x=2/3 and x is in quadrant 4 then value of sin x/2 is  -√(1/6), option C is correct.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To find sin(x/2), we can use the half-angle formula for sine:

sin(x/2) = ±√[(1 - cos x)/2]

Since x is in quadrant 4, cosine is positive and sine is negative. We are given that cos x = 2/3

so we can substitute this value into the formula:

sin(x/2) = -√[(1 - 2/3)/2]

sin(x/2) = -√(1/6)

Hence, if cos x=2/3 and x is in quadrant 4 then sin x/2 is  -√(1/6)

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Answer:

17. 50

18. 150

19. 240

20. 20

21. 60

22. 240

23. 150

24. -240

25. 222

26. 75

27. 300

28. 340

29. 175

30. 265

31. 298

32. 118

Step-by-step explanation:

How you find co-terminal is by adding or subtracting 360 degrees to the value you are given.

If it is a positive number like #18. all you do is subtract 510 - 360 = 150 until you get to a value between 0 degrees and 360 degrees.

The same thing applies to negative numbers. Like #21. You will add 360 + (-660) until you get to a number between 0 degrees and 360 degrees.

-660 + 360 = -300 (this is not a value in between 0 and 360 so we must add 360 again)

-300 + 360 = 60 (this is a value in between 0 and 360) (this is the co-terminal angle)

That is the idea of finding co-terminal angles.

Answer: 5 units

Step-by-step explanation:

Answer:

the (2x) obviously because it is close to an acute angle and the (13x) is closer to a right angle

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Percent means out of 100

We have 3/25

Multiply the top and bottom by 4

12/100

The percent is 12

Final answer:

Based on the estimate provided, 12% of men are left-handed, which is calculated by dividing 3 by 25 and then multiplying the result by 100.

Explanation:

To calculate the percentage of men who are left-handed based on the estimate that 3 out of every 25 men are left-handed, you can use the following steps:

Therefore, based on the given estimate, 12% of men are left-handed.

Answer:

False, since x values cannot have more than one y value.

Step-by-step explanation:

Because if you were to plot the points on a graph, and do the vertical line test, there will be points that cross one another making it not a function.

Hope I Helped

The false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

It is given that:

A box plot is shown in the picture;

As we know,

The interquartile range(IQR):

IQR = Q3 - Q1

IQR = 50 - 30

IQR = 20

From the box plot:

The median of the upper half of the data is 49.

The median of the data is 37.

Three-fourths of the data is less than 49.

Thus, the false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.

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Answer: 14

Step-by-step explanation:

The number of fraternity members taking physics but not mathematics is 27, calculated using inclusion-exclusion principle: 18 members take math, 5 take both math and physics, and 8 take neither.

Let's use the principle of inclusion-exclusion to solve this problem.

Total fraternity members (n) = 40

Members taking mathematics (M) = 18

Members taking both mathematics and physics (B) = 5

Members taking neither mathematics nor physics (N) = 8

To find the number of members taking physics but not mathematics (P).

We can start by using the formula for the number of elements in the union of two sets:

n(M ∪ P) = n(M) + n(P) - n(B)

Since the total members are 40, the equation becomes:

18 + n(P) - 5 = 40

Solving for n(P):

n(P) = 40 - 18 + 5

n(P) = 27

Therefore, 27 members take physics but not mathematics.

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Answer:

6.4cm

Step-by-step explanation:

The radius of a circle with a diameter of 12.8 cm is 6.4 cm.

The diameter of a circle is twice the length of its radius, so to find the radius of a circle given its diameter, you simply divide the diameter by 2.

In this case, the diameter is 12.8 cm, so the radius would be 12.8 cm / 2 = 6.4 cm.

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The cost of each raffle ticket was $5.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Amount donated by Aldon = $40

Number of tickets sold by Aldon = 12

Amount denoted by Jamal = $25

Number of tickets sold by Jamal = 15

Let x be the cost of each raffle ticket.

So, Cost of tickets sold by Aldon = 12x

Cost of tickets sold by Jamal = 15x

So, Total amount raised by Aldon = 12x + 40

Total amount raised by Jamal = 15x + 25

∵ Aldon and Jamal raised the same amount of money for the school fundraiser

⇒ 12x + 40 = 15x + 25

Taking aliketerms together we get,

15x - 12x = 40 - 25

⇒ 3x = 15

Dividing both side by 3 we get,

x = $5

which is the required cost of each raffle ticket.

Thus, the cost of each raffle ticket was $5.

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Answer:

164 adult tickets

Step-by-step explanation:

164×3 = 492 tickets

Really hope this helped! :)

Final answer:

A total of 123 adult tickets were sold for the school play, with the total number of tickets sold being 492 and student tickets being three times the number of adult tickets.

Explanation:

To solve the problem of how many adult tickets were sold at the school play when a total of 492 tickets were sold and the number of student tickets was three times the number of adult tickets, we set up a system of equations. Let A be the number of adult tickets and S be the number of student tickets sold.

Steps to solve this question:

The total number of tickets sold was 492: A + S = 492

The number of student tickets was three times the number of adult tickets: S = 3A

We can substitute the second equation into the first to find the number of adult tickets:

A + 3A = 492

4A = 492

A = 492 / 4

A = 123

Therefore, 123 adult tickets were sold for the school play.

Answer:

the square root of -25 is 5i

Answer:

5i

Step-by-step explanation

All negative roots have i, which is an imaginary number.

i^2=-1.

Following this, the square root of -25 is 5i.

To double check:

5i*5i=5*5*i*i

25*-1=-25

Answer:

x = 10

Step-by-step explanation:

3x + 55 = 9x - 5  (add 5 to both sides)

3x + 55 + 5 = 9x - 5 + 5

3x + 60 = 9x  (subtract 3x from both sides)

60 = 9x - 3x

60 = 6x (rearrange)

6x = 60   (divide both sides by 6)

x = 60/6

x = 10

Answer:

x=10

Step-by-step explanation:

[tex]\mathrm{Subtract\:}55\mathrm{\:from\:both\:sides}\\3x+55-55=9x-5-55[/tex]

[tex]\mathrm{Simplify}\\3x=9x-60[/tex]

[tex]\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\3x-9x=9x-60-9x[/tex]

[tex]\mathrm{Simplify\:}again\\-6x=-60[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-6\\\frac{-6x}{-6}=\frac{-60}{-6}[/tex]

[tex]\mathrm{\:Simplify\:one\:more\:time}\\x=10[/tex]

I hope this helps you out!

Have a wonderful afternoon!

Answer:

5.14

Step-by-step explanation

6/x = 42/36

42x= 216

x= 5.14

Answer:

[tex]22\ m < x < 74\ m[/tex]

Step-by-step explanation:

Let

x ----> the length for the third side

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) [tex]26+48> x[/tex]

solve for x

[tex]74> x[/tex]

Rewrite

[tex]x < 74\ m[/tex]

2) [tex]26+x>48[/tex]

solve for x

subtract 26 both sides

[tex]x> 22\ m[/tex]

therefore

The range of  possible lengths, in meters, for the third side is equal to

[tex]22\ m < x < 74\ m[/tex]

The range of the possible length of the third side of the triangle is 22 to 74 (exclusive)

Assume the lengths of a triangle are x, y and z.

The following are the possible inequalities that relate the side lengths

[tex]x + y > z[/tex]

[tex]y + z > x[/tex]

[tex]x + z > y[/tex]

The unknown side length is x.

So, we have:

[tex]x + 26 > 48[/tex]

[tex]48 + 26 > x[/tex]

[tex]x + 48 > 26[/tex]

Solve for x in the three inequalities

[tex]x + 26 > 48[/tex]

[tex]x > 22[/tex]

[tex]48 + 26 > x[/tex]

[tex]74 > x[/tex]

[tex]x + 48 > 26[/tex]

[tex]x > -22[/tex]

The values of x cannot be negative.

So, we ignore the inequality [tex]x > -22[/tex]

We are left with

[tex]74 > x[/tex] and [tex]x > 22[/tex]

Combine the inequalities

[tex]74 > x > 22[/tex]

Rewrite as:

[tex]22 < x < 74[/tex]

Hence, the range of the possible length is 22 to 74 (exclusive)

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The calculated length of the arc MPN is 79/9π units

Finding the length of arc MPN

From the question, we have the following parameters that can be used in our computation:

Central angle = 360 - 44 = 316 degrees

Radius = 5 units

Using the above as a guide, we have the following:

arc MPN = central angle/180 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

arc MPN = 316/180 * π * 5

Evaluate

arc MPN = 79/9π

Hence, the length of the arc is 79/9π units

Answer:

A) y= -8/5x -3

Step-by-step explanation:

This is your current equation: y= -8/5x + b. I would plug in your point to the equation. It should look like this: 5= -8/5(-5)+b. Multiply -8/5 by -5 to get 8. This is what you should have: 5=8+b. Subtract 8 from both sides to get -3=b. So, this is your final answer: y= -8/5x -3. So, A is the correct answer. Hope this helped!

Answer:

  6

Step-by-step explanation:

The center of the circle is the midpoint of the diameter. The midpoint can be found by averaging the coordinates of the end points:

  ((-4, 2) +(12, 10))/2 = ((-4+12)/2, (2+10)/2) = (4, 6)

The y-coordinate of the center is 6.

The center of the circle has a y-coordinate of 6, determined by averaging the y-coordinates (2+10)/2 of the diameter's endpoints (-4,2) and (12,10).

The y-coordinate for the center of a circle can be determined by finding the midpoint of the y-coordinates of the diameter's endpoints. Given the endpoints (-4,2) and (12,10), the midpoint can be found by averaging the y-coordinates: (2 + 10) / 2 = 12 / 2 = 6. Therefore, the y-coordinate of the center of the circle is 6.

Area of the square = side x side = side ^2

therefore to find a length of one side = Square root of the 441

sqrt of 441 = 21 cm

so the perimeter of a square is 21 x 4 = 84 cm

Answer:

3/(30×30×30) = 3/27000 = 0.0001 or 0.01%

Step-by-step explanation:

Answer:

here we have 3 dials in the slot machines and each dial has 30 position

so probability of getting a number of the each dial   =  

30

1

​

since all dials are independent so probability of getting same number would be

P ( getting jack pot) =  

30

1

​

30

1

​

30

1

​

   =    

27000

1

​

   = 0.003% option D is correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rate of interest is 5%.

Time =3years

Amount =$852

Then, we need to find P

Generally compound interest is given as

A=P(1+r/n)^nt

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period=12

t=number of time periods elapsed

A=P(1+r/n)^nt

852=P(1+0.05/12)^(12×5)

852=P(1+0.004167)^60

852=P(1.004167)^60

852=1.2834P

Then, P=852/1.2834

P=$663.88

Then the principal amount invested is $663.88

Approximately $664

Answer:

Step-by-step explanation:

(a+1)+(b-2)i=6+7i

⇔

a + 1 = 6

and

b - 2 = 7

⇔

a = 5

and

b = 9

Answer:

40 Miles Per Hour

Step-by-step explanation:

If this is traveling 100 Miles in 2.5 hours...

100/2.5 = 40

You would have to go 40 Miles Per Hour.

Answer:40

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

9 Chocolate cupcakes, 9/12

3 Cupcakes are the remaining cupcakes, over 12 it's 3/12

Then Simplify, 3/12

by dividing

3 divided by 3 equals 1

12 divided by 3 equals 4

then use the simplified version 1/4

To check:

add 3/12 + 9/12

and it equals all 12 cupcakes

Final answer:

There are 3 cupcakes with vanilla frosting out of 12 total, resulting in the fraction 3/12, which simplifies to 1/4 for the cupcakes with vanilla frosting.

Explanation:

The student's question is asking us to find what fraction of the cupcakes have vanilla frosting. Mindy buys 12 cupcakes in total and 9 of them have chocolate frosting. To find how many have vanilla frosting, we subtract the chocolate frosted cupcakes from the total:

12 cupcakes - 9 chocolate frosted cupcakes = 3 vanilla frosted cupcakes

To express this as a fraction, we take the number of vanilla frosted cupcakes (which is 3) over the total number of cupcakes (which is 12).

Therefore, the fraction of cupcakes that have vanilla frosting is 3/12, which can be simplified to 1/4.